Plane and Solid Geometry |
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Page 6
... greater than any of its parts . 9. The whole is equal to the sum of all its parts . 35 . SYMBOLS AND ABBREVIATIONS . is ( or are ) greater than . Def . < is ( or are ) less than . Ax . is ( or are ) equivalent to . Нур . definition ...
... greater than any of its parts . 9. The whole is equal to the sum of all its parts . 35 . SYMBOLS AND ABBREVIATIONS . is ( or are ) greater than . Def . < is ( or are ) less than . Ax . is ( or are ) equivalent to . Нур . definition ...
Page 11
... greater than a right angle and D less than a straight angle is called an obtuse angle ; as , angle AOD ( Fig . 14 ) . FIG . 13 . FIG . 14 . 70. An angle greater than a straight angle and less than two straight angles is called a reflex ...
... greater than a right angle and D less than a straight angle is called an obtuse angle ; as , angle AOD ( Fig . 14 ) . FIG . 13 . FIG . 14 . 70. An angle greater than a straight angle and less than two straight angles is called a reflex ...
Page 14
... greater than the angle ABC . H с F M E A B FIG . 20 . FIG . 21 . 80. If we have the angles ABC and DEF ( Fig . 20 ) , and place the vertex E on B and the side ED on BC , so that the angle DEF takes the position CBH , the angles DEF and ...
... greater than the angle ABC . H с F M E A B FIG . 20 . FIG . 21 . 80. If we have the angles ABC and DEF ( Fig . 20 ) , and place the vertex E on B and the side ED on BC , so that the angle DEF takes the position CBH , the angles DEF and ...
Page 22
... greater than the sum of two other lines similarly drawn , but included by them . A E B Let CA and CB be two lines drawn from the point C to the extrem- ities of the straight line AB . Let OA and OB be two lines similarly drawn , but ...
... greater than the sum of two other lines similarly drawn , but included by them . A E B Let CA and CB be two lines drawn from the point C to the extrem- ities of the straight line AB . Let OA and OB be two lines similarly drawn , but ...
Page 23
... greater than CG . To prove that OE > OG . Proof . Take CF equal to CG , and draw OF . Then = OF OG , $ 95 two ... greater cuts off on the line the greater segment from the foot of the perpendicular . PARALLEL LINES . 103. DEF . Two ...
... greater than CG . To prove that OE > OG . Proof . Take CF equal to CG , and draw OF . Then = OF OG , $ 95 two ... greater cuts off on the line the greater segment from the foot of the perpendicular . PARALLEL LINES . 103. DEF . Two ...
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Common terms and phrases
ABCD AC² adjacent angles altitude angles are equal apothem axis bisector bisects called centre chord circumference circumscribed coincide construct cylinder denote diagonals diameter dihedral angles divided Draw equiangular equidistant equilateral triangle equivalent exterior angle feet Find the area Find the locus frustum given circle given line given point given straight line greater Hence homologous homologous sides hypotenuse inches inscribed intersecting isosceles triangle lateral area lateral edges limit middle point number of sides opposite parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedron prism prismatoid Proof proportional prove Q. E. D. PROPOSITION quadrilateral radii radius ratio rectangle regular polygon respectively rhombus right angle right circular right triangle segments similar slant height sphere spherical square surface tangent tetrahedron THEOREM trapezoid triangle ABC triangle is equal trihedral vertex vertices
Popular passages
Page 274 - If two planes are perpendicular to each other, a straight line drawn in one of them, perpendicular to their intersection, is perpendicular to the other.
Page 50 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Page 66 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Page 41 - If two angles of a triangle are unequal, the sides opposite are unequal, and the greater side is opposite the greater angle.
Page 169 - In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side.
Page 360 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 71 - The sum of the perpendiculars dropped from any point in the base of an isosceles triangle to the legs, is equal to the altitude upon one of the arms.
Page 156 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 71 - The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle (Fig.
Page 383 - Hence the two last are right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is at right angles to the base, and bisects the vertical angle.